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 Volume and Surface Area Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

 

 

I. CUBOID

   Let length=l, breadth =b and height =h units. Then,

1. Volume = (l x b x h)

2. Surface area = 2(lb +bh + lh) sq.units

3. Diagonal =l2+b2+h2 units

 

 

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume = a3 cubic units.

2. Surface area = 6a2 sq.units

3. Diagonal = 3a units

 

 

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume = πr2h cubic units 

2. Curved surface area = 2πrh sq.units

3. Total surface area = 2πrh+2πr2 sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, l=h2+r2 units

 

2. Volume = 13πr2h cubic units.

 

3. Curved surface area = πrlsq.units 

 

4. Total surface area = πrl+πr2sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =43πr3 cubic units

2. Surface area = 4πr2 sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = 23πr3 cubic units.

2. Curved surface area = 2πr2 sq.units

3. Total surface area = 3πr2 sq.units

 

Q:

A cone of radius 7 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 3.5 cm. What will be the height of water in this vessel?

A) 16 cm B) 32 cm
C) 5.33 cm D) 8 cm
 
Answer & Explanation Answer: A) 16 cm

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Q:

A point P lying inside a triangle is equidistant from the vertices of the triangle. Then the triangle has P as its

A) Centroid B) Incentre
C) Orthocentre D) Circumcentre
 
Answer & Explanation Answer: D) Circumcentre

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Q:

In an isosceles triangle ABC, AB = AC, XY || BC. If ∡A = 30, then ∡BXY = 

A) 75° B) 30°
C) 150° D) 105°
 
Answer & Explanation Answer: D) 105°

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Q:

PT is a tangent to a circle with centre O and radius 6 cm . If PT is 8 cm then length of OP is

A) 10 cm B) 12 cm
C) 16 cm D) 9 cm
 
Answer & Explanation Answer: A) 10 cm

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Q:

Which of the following is not true for a rhombus?

A) All sides are congruent B) Opposite sides are parallel
C) Diagonals are equal D) Diagonals bisect each other at right angles
 
Answer & Explanation Answer: C) Diagonals are equal

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Q:

The radius of a cylindrical milk container is half its height and surface area of the inner part is 616 sq.cm. The amount of milk that the container can hold, approximately, is [ Use : √5 = 2.23 and π = 22/7 ]

A) 1.42 litres B) 1.53 litres
C) 1.71 litres D) 1.82 litres
 
Answer & Explanation Answer: B) 1.53 litres

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Q:

PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?

A) 55 B) 60
C) 70 D) 90
 
Answer & Explanation Answer: C) 70

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Q:

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?

A) 12 B) 14
C) 16 D) 28
 
Answer & Explanation Answer: D) 28

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